We investigate all pure quantum-electrodynamics corrections to the np --> 1s, n = 2-4 transition energies of pionic hydrogen larger than 1 meV, which requires an accurate evaluation of all relevant contributions up to order alpha 5. These values are needed to extract an accurate strong interaction shift from experiment. Many small effects, such as second-order and double vacuum polarization contribution, proton and pion self-energies, finite size and recoil effects are included with exact mass dependence. Our final value differs from previous calculations by up to approximate to 11 ppm for the 1s state, while a recent experiment aims at a 4 ppm accuracy.
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